Representation type of finite quiver Hecke algebras of type $A_{\ell }^{(1)}$ for arbitrary parameters

Abstract

We give Erdmann-Nakano type theorem for the finite quiver Hecke algebras $R^{{\Lambda }_0}(\beta )$ of affine type $A_{\ell }^{(1)}$. Note that each finite quiver Hecke algebra lies in one parameter family, and the original Erdmann-Nakano theorem studied the finite quiver Hecke algebra at a special parameter value. We study the general case in our paper. Our result shows in particular that their representation type does not depend on the parameter. Moreover, when the parameter value is nonzero, we show that finite quiver Hecke algebras of tame representation type are biserial algebras.

54 pages, (v2) We have added counterexamples to Pogorzaly's result and modified some parts in sections 6 and 7

References in corpus (3)

• 2-Kac-Moody algebras
• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• Rigidity of tilting complexes and derived equivalence for self-injective algebras

Cited by in corpus (1)

• Mapping cones in the bounded derived category of a gentle algebra